Log X Is Just A Number
June 14th, 2008 | by limeehai |I happened to come across an interesting mistake made by a maths student.
The mistake inter-mixed the principles of algebra with logarithm.
The maths question is to solve the value of x given the expression:
2+ log (5x - 1) = log 3x
The expression, after transferring the “log (5x -1)” to the right side of the “=”, became
2 = log 3x - log (-5x + 1) !
Spotted the mistake done ?
Why was the “log (-5x + 1)” in that form?
The correct expression should be 2 = log 3x - log (5x - 1).
What actually went inside the student’s mind was confusion between algebra and logarithm. He did not understand the concept of “logging” the (5x -1).
Log X is always a number!
Similarly log (5x - 1) is also a number.
Therefore log (5x - 1) moves as a number, same as in moving algebraic term.
If we have 2 + (x-a) = y, re-arranging the expression, gives us 2 = y - ( x-a).
The term “x-a” is taken as a whole, with change in the sign of (x -a) and not including that of the individual internal “a” and “x”. This is basic algebra.
Moving log (5x - 1) is the same. Being a number, it operates equivalent to the algebraic manipulation.
The log (5x -1) is thus taken as a whole and sign change affects only the term as a whole. It does not affect the individual internal “5x” and “-1″!
Part of learning maths is following rules and principles.
The mistake made by the student was a reflection of correct algebraic change, but in the wrong sense. “Log” had convert the term into a number, and that was the mistake not captured.
2 Responses to “Log X Is Just A Number”
By Leena on Jun 15, 2008 | Reply
I have mostly seen the same with sin x and cos x.
Also it is not very extraordinary to see that log(5x-1)=log5x-log1.
In my experience the original character of logarithms is very hard for the students. Even the expression is hard to connect to exponent functions.
By Lim Ee Hai on Jun 15, 2008 | Reply
True, this common mistake does apply to other maths areas like the trigonometry and exponential. I believe when the students learn maths, the foundation has to be really re-inforced. Time should not be spared in this instance for the good of their “future” in learning maths. The principles and concepts in manipulating algebraic terms and other basics are eventually the settings for further progress. Maths principles understanding is therefore crucial to ease learning.